Nuprl Lemma : proj-permute_wf
∀[n:ℕ]. ∀[p:ℙ^n]. ∀[f:ℕn + 1 ⟶ ℕn + 1]. proj-permute(p;f) ∈ ℙ^n supposing Surj(ℕn + 1;ℕn + 1;f)
Proof
Definitions occuring in Statement :
proj-permute: proj-permute(p;f),
real-proj: ℙ^n,
surject: Surj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
real-proj: ℙ^n,
nat: ℕ,
so_lambda: λ2x.t[x],
real-vec: ℝ^n,
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
proj-permute: proj-permute(p;f),
subtype_rel: A ⊆r B,
surject: Surj(A;B;f),
all: ∀x:A. B[x],
compose: f o g,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
exists_wf,
int_seg_wf,
rneq_wf,
int-to-real_wf,
surject_wf,
real-proj_wf,
nat_wf,
compose_wf,
real_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
extract_by_obid,
isectElimination,
natural_numberEquality,
addEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionExtensionality,
isect_memberEquality,
functionEquality,
productElimination,
dependent_functionElimination,
dependent_pairFormation,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:\mBbbP{}\^{}n]. \mforall{}[f:\mBbbN{}n + 1 {}\mrightarrow{} \mBbbN{}n + 1]. proj-permute(p;f) \mmember{} \mBbbP{}\^{}n supposing Surj(\mBbbN{}n + 1;\mBbbN{}n + 1;f)
Date html generated:
2017_10_05-AM-00_20_50
Last ObjectModification:
2017_06_17-AM-10_10_12
Theory : inner!product!spaces
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