Nuprl Lemma : sg-op-sep
∀sg:s-GroupStructure. ∀x1,y1,x2,y2:Point. ((x1 y1) # (x2 y2) ⇒ (x1 # x2 ∨ y1 # y2))
Proof
Definitions occuring in Statement :
s-group-structure: s-GroupStructure,
sg-op: (x y),
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
s-group-structure: s-GroupStructure,
record+: record+,
member: t ∈ T,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
or: P ∨ Q,
so_apply: x[s],
sg-op: (x y)
Lemmas referenced :
subtype_rel_self,
ss-point_wf,
all_wf,
ss-sep_wf,
or_wf,
s-group-structure_subtype1,
sg-op_wf,
s-group-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
cut,
hypothesis,
applyEquality,
tokenEquality,
introduction,
extract_by_obid,
isectElimination,
functionEquality,
lambdaEquality,
because_Cache,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}sg:s-GroupStructure. \mforall{}x1,y1,x2,y2:Point. ((x1 y1) \# (x2 y2) {}\mRightarrow{} (x1 \# x2 \mvee{} y1 \# y2))
Date html generated:
2017_10_02-PM-03_24_34
Last ObjectModification:
2017_06_23-AM-11_13_49
Theory : constructive!algebra
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