Nuprl Lemma : topfuneq-equiv-ext
∀X,Y:Space. EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g))
Proof
Definitions occuring in Statement :
topfuneq: topfuneq(X;Y;f;g),
topfun: topfun(X;Y),
topspace: Space,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
squash: ↓T,
or: P ∨ Q,
guard: {T},
prop: ℙ,
has-value: (a)↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
strict4: strict4(F),
uimplies: b supposing a,
top: Top,
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
uall: ∀[x:A]. B[x],
topeq-equiv,
topeq_transitivity,
topeq_inversion,
topeq_weakening,
topfuneq-equiv,
tfunequiv: tfunequiv(X;Y),
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
member: t ∈ T
Lemmas referenced :
strict4-spread,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-spread,
topfuneq-equiv,
topeq-equiv,
topeq_transitivity,
topeq_inversion,
topeq_weakening
Rules used in proof :
because_Cache,
inlFormation,
imageElimination,
imageMemberEquality,
inrFormation,
applyExceptionCases,
hypothesisEquality,
closedConclusion,
baseApply,
callbyvalueApply,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
isectElimination,
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}X,Y:Space. EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g))
Date html generated:
2018_07_29-AM-09_48_39
Last ObjectModification:
2018_06_21-AM-10_38_32
Theory : inner!product!spaces
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