Nuprl Lemma : sg-op_functionality
∀[sg:s-GroupStructure]. ∀[x1,y1,x2,y2:Point]. ((x1 y1) ≡ (x2 y2)) supposing (x1 ≡ x2 and y1 ≡ y2)
Proof
Definitions occuring in Statement :
s-group-structure: s-GroupStructure,
sg-op: (x y),
ss-eq: x ≡ y,
ss-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
sg-op-sep,
ss-sep_wf,
sg-op_wf,
s-group-structure_subtype1,
ss-eq_wf,
ss-point_wf,
s-group-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
unionElimination,
voidElimination,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[sg:s-GroupStructure]. \mforall{}[x1,y1,x2,y2:Point]. ((x1 y1) \mequiv{} (x2 y2)) supposing (x1 \mequiv{} x2 and y1 \mequiv{} y2)
Date html generated:
2017_10_02-PM-03_24_36
Last ObjectModification:
2017_06_23-AM-11_14_58
Theory : constructive!algebra
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