Nuprl Lemma : proj-eq_inversion
∀[n:ℕ]. ∀[a,b:ℙ^n]. b = a supposing a = b
Proof
Definitions occuring in Statement :
proj-eq: a = b,
real-proj: ℙ^n,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
proj-eq: a = b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nat: ℕ,
real-proj: ℙ^n,
real-vec: ℝ^n,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
int_seg_wf,
req_witness,
rmul_wf,
all_wf,
req_wf,
real-proj_wf,
nat_wf,
req_weakening,
req_functionality,
req_inversion
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
applyEquality,
because_Cache,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbP{}\^{}n]. b = a supposing a = b
Date html generated:
2017_10_05-AM-00_18_30
Last ObjectModification:
2017_06_17-AM-10_07_44
Theory : inner!product!spaces
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