Nuprl Lemma : proj-eq_weakening
∀[n:ℕ]. ∀[a,b:ℙ^n]. a = b supposing a = b ∈ ℙ^n
Proof
Definitions occuring in Statement :
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
proj-eq: a = b,
all: ∀x:A. B[x],
real-proj: ℙ^n,
real-vec: ℝ^n,
nat: ℕ
Lemmas referenced :
proj-eq_wf,
squash_wf,
true_wf,
iff_weakening_equal,
req_witness,
rmul_wf,
int_seg_wf,
equal_wf,
real-proj_wf,
nat_wf,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
setElimination,
rename,
addEquality,
isect_memberEquality,
lambdaFormation
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbP{}\^{}n]. a = b supposing a = b
Date html generated:
2017_10_05-AM-00_18_39
Last ObjectModification:
2017_06_17-AM-10_07_56
Theory : inner!product!spaces
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