Nuprl Lemma : ap-action-op
∀[g:s-Group]. ∀[n:SeparationSpace]. ∀[a:sg-action(g;n)]. ∀[f,h:Point]. ∀[x:Point]. f(h(x)) ≡ (f h)(x)
Proof
Definitions occuring in Statement :
ap-action: h(x),
sg-action: sg-action(g;n),
s-group: s-Group,
sg-op: (x y),
ss-eq: x ≡ y,
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sg-action: sg-action(g;n),
and: P ∧ Q,
cand: A c∧ B,
so_lambda: λ2x.t[x],
s-group: s-Group,
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
ap-action: h(x),
squash: ↓T,
ss-eq: x ≡ y,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
sq_stable__ss-eq,
ap-action_wf,
all_wf,
ss-point_wf,
ss-eq_wf,
sg-op_wf,
sg-id_wf,
ss-sep_wf,
s-group-structure_subtype1,
s-group_subtype1,
subtype_rel_transitivity,
s-group_wf,
s-group-structure_wf,
separation-space_wf,
sg-action_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
productElimination,
hypothesis,
independent_pairFormation,
dependent_set_memberEquality,
productEquality,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
isect_memberEquality,
instantiate,
independent_isectElimination,
voidElimination
Latex:
\mforall{}[g:s-Group]. \mforall{}[n:SeparationSpace]. \mforall{}[a:sg-action(g;n)]. \mforall{}[f,h:Point]. \mforall{}[x:Point].
f(h(x)) \mequiv{} (f h)(x)
Date html generated:
2017_10_02-PM-03_25_38
Last ObjectModification:
2017_07_03-PM-02_00_35
Theory : constructive!algebra
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