Nuprl Lemma : proj-sep_functionality
∀n:ℕ. ∀a1,b1,a2,b2:ℙ^n. (a1 = a2 ⇒ b1 = b2 ⇒ {a1 ≠ b1 ⇐⇒ a2 ≠ b2})
Proof
Definitions occuring in Statement :
proj-eq: a = b,
proj-sep: a ≠ b,
real-proj: ℙ^n,
nat: ℕ,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
not: ¬A,
false: False,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
not-proj-sep-iff-proj-eq,
proj-sep_wf,
proj-eq_wf,
real-proj_wf,
nat_wf,
proj-sep-or,
proj-eq_inversion
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_pairFormation,
independent_functionElimination,
isectElimination,
unionElimination,
voidElimination,
because_Cache,
independent_isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a1,b1,a2,b2:\mBbbP{}\^{}n. (a1 = a2 {}\mRightarrow{} b1 = b2 {}\mRightarrow{} \{a1 \mneq{} b1 \mLeftarrow{}{}\mRightarrow{} a2 \mneq{} b2\})
Date html generated:
2017_10_05-AM-00_19_06
Last ObjectModification:
2017_06_18-PM-03_33_43
Theory : inner!product!spaces
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